A smaller number of USA troops operate in Afghanistan under a counter-terrorism mission.
This was the third bomb attack in the city in three days, all of them claimed by Islamic State's local affiliate, Khorasan Province (ISKP).
Two Americans, an Army Green Beret and explosive ordnance disposal (EOD) specialist, were killed during a mission in Kunduz province last month.
"The wounded service members were evacuated and are receiving medical care", Resolute Support said in a statement. The explosion occurred near Bagram air base, 50km (31 miles) north of the capital Kabul.
The latest deaths brings the number of USA service members' deaths in Afghanistan to seven this year, and a total of 68 since Jan 2015.
In accordance with Department of Defense policy, the identities of the killed and wounded are being withheld pending notification of next-of-kin. He leaves behind his wife, Shannon, and three daughters.
Following an assessment on scene, it was determined that the contractor, an Afghan national, had received initial treatment with other injured civilians, according to Operation Resolute Support officials.
Four were passers-by and the fifth was a driver of a auto going down the road, said Abdul Raqib Kohistani, the Bagram district police chief.
There are about 14,000 USA forces in Afghanistan, supporting embattled Afghan forces as they struggle on two fronts - facing a resurgent Taliban who now hold sway over nearly half the country and also the Islamic State affiliate, which has sought to expand its footprint in Afghanistan even as its self-proclaimed "caliphate" has crumbled in Syria and Iraq.
While US officials have said that peace talks with the Taliban have made progress, they have yet to finalize any agreements and intense fighting between the government and the insurgency continues. But the Taliban say they will not recognize any government official attending the gathering as a representative of the Kabul government, only as an individual Afghan participant. The insurgents dismiss the Afghan government as a USA puppet.
"USA service members have sacrificed their lives in Afghanistan to keep us safe and no cowardly act of terror will impede our efforts to achieve peace", Pompeo said in a statement posted in his Twitter account.